1. Field of Invention
This invention relates to a method of optimizing the effects of a shim on magnetic field in an imaging apparatus or a multi-sample spectrometer; and more particularly, to such a method for determining values of currents applied to the coils of the shim so as to enable homogeneous magnetic field to be applied to a plurality of cells of a probe used therein.
2. Discussion of the Related Art
In the art, there is provided an imaging system, such as those utilizing nuclear magnetic resonance (NMR), wherein a radio frequency (RF) probe having one or more cells therein is used to obtain data from one or more samples. Each cell has a space for holding a sample, such as a mouse. The plurality of cells are disposed within a space of a magnet, which could be a superconducting magnet, an electro magnet or a permanent magnet, which provides a static magnetic field within which the cells are disposed. The RF signal is provided, for example, by a common RF power source to each cell, through a power divider, which transmits an RF signal to each cell. The resulting imaging signal is received by each cell and is coupled through a transmit/receive (T/R) circuit to a separate receiver, detector and data storage memory, all of which are known in the art. A plurality of probes, each having one or more cells, can also be used.
The static magnetic field, contained within the sample space, usually requires adjustment for desired properties, such as magnetic homogeneity. This can be done by a shim system of one or more coils which are located at different positions with respect to the magnetic field to produce magnetic field gradients used to compensate for spatial variations of the magnetic field.
The shim coils need to be adjusted to produce uniform magnetic field value Bo to all of the probe cells in order to produce optimal results.
One method for shim adjustment is to combine the RF output signals for each cell and couple the combined RF signals to a common receiver. With use of a simulated sample, such as a simulated mouse, in each cell, the plurality of shim coils can be adjusted to obtain overall signal height or narrowest overall line width, as desired. Another method, and similar to the foregoing method, is to combine the signals after detection and use the resulting signal height or line width to determine the optimal shim setting. In order to avoid problems with signal phasing, the absolute signal amplitude can be used instead of a phase adjusted absorption mode response.
In liquid spectroscopy, wherein multiple probe cells are used with multiple shim coils for adjustment of common signals, similar problems exist.
The foregoing shim adjustment methods have all been found to have deficiencies and leave much to be desired. In these cases, adjustment requires repeated optimization steps. Also, adjustment of one shim coil changes the optimization required of other shim coils so that it is difficult to obtain the desired degree of optimization for all of the shim coils without requiring an undue number of readjustment steps to achieve the desired optimization. Also, there is continued uncertainty of whether the best fit or adjustment is ever obtained. Thus, there is, in the art, uncertainty when an adjustment procedure should be terminated.
Accordingly, an object of the invention is to overcome the aforementioned and other deficiencies and disadvantages of the prior art.
Another object is to optimize the effects of the shim system on magnetic fields to provide uniformity of magnetic field values at different probe cells disposed therein.
A further object is to obtain the same value of resonant frequency of simulated samples at different probe cells disposed in a static magnetic field.
A further object is to provide optimal shim settings in a liquid spectroscopy system utilizing a probe having a plurality of cells.
Another object is to optimize shim settings so that a minimum amount of errors occurs in a magnetic field at different probe cells.
The foregoing and other objects are attained in the invention method which is based on the mathematical relation of the frequency in a cell Fj depends on the linear relationship with currents I1, I2, . . . IN of the shim coils 1, 2, . . . N, with a constant term Gj, the frequency being with no currents in the shim coils. This linear relationship is expressed by the following;       F    j    =            G      j        +                  ∑                  k          =          1                N            ⁢                        a          jk                ⁢                              I            k                    .                    
One object of the invention is to find the shim current values that will result in the same resonant frequency at each cell.
This is done by first measuring the resonant frequency of the cells when no current is applied to the shim coils giving the values of Gj, and then, for each cell j measuring the change of the resonant frequency (Fjxe2x88x92Gj) when a current is applied to one shim coil k without any current being applied to the other shim coils. The change in frequency (Fjxe2x88x92Gj) divided by the current Ik that produced that change gives a sensitivity factor ajk of the one cell of the selected shim coil k. For the selected cell j the process is carried out for the current in each shim coil k. The process is repeated for each cell j giving a matrix of sensitivity factors ajk. The shim currents values required to produce the same frequency in each cell are calculated by a matrix multiplication of the inverse of the sensitivity matrix ajk and difference of the target frequency and initial frequency of each cell Fjxe2x88x92Gj.
For the case, when the number of RF probe cells M is greater than the number of shim coils N, the matrix of values is operated on to obtain the least square of errors thereby minimizing the difference of the magnetic field values from the desired values Fjxe2x88x92Gj.
A feature of the invention is a method of optimizing effects of shims on adjusting a, magnetic field applied to a plurality of cells of a probe, comprising the steps of determining a value of current which is applied to a plurality of shim coils so that the resonant frequency of each cell of the probe is substantially the same and so that the plurality of cells of the probe are subjected to a uniform magnetic field.
Another feature is the method wherein the value of the current is determined using the following steps: measuring resonant frequency of each of the probe cells disposed in the magnetic field without any current being supplied to the plurality of coils of the shim, thereby to obtain G1, G2, . . . , GM, wherein M is the number of the probe cell; measuring resonant frequency of a first cell of the probe using a current I1, applied to a first shim coil and without any current being applied to the other shim coils to obtain F11, wherein the first subnumber is the number of the probe cell and the second subnumber is the number of the shim coil which is energized by current I1; measuring resonant frequency of a second cell with current I1 being applied to a first shim coil and without any current being applied to the other shim coils, to obtain F21. This process is contained for the remaining cells up through FMI. The process is then repeated measuring the frequencies of the cells for a current I2 in shim coil 2, with no other shim currents present. Continuing this process through all shim coils leads to a matrix of values Fjk. The sensitivity matrix ajk is then found using the following:       a          j      ⁢              xe2x80x83            ⁢      k        =                    F                  j          ⁢                      xe2x80x83                    ⁢          k                    -              G        j                    I      k      
wherein the matrix becomes;   A  =      [                                        a            11                                                a            12                                    …                                      a                          1              ⁢                              xe2x80x83                            ⁢              N                                                                        a            21                                                a            22                                    …                                      a                          2              ⁢                              xe2x80x83                            ⁢              N                                                            ⋮                          ⋮                                      xe2x80x83                                    ⋮                                                  a            M1                                                a            M2                                    …                                      a                          M              ⁢                              xe2x80x83                            ⁢              N                                            ]  
The frequencies at each cell j, Fj and current in each shim k, Ik in matrix form are:   F  =                    [                                                            F                1                                                                                        F                2                                                                        ⋮                                                                          F                M                                                    ]            ⁢              xe2x80x83            ⁢      G        =                            [                                                                      G                  1                                                                                                      G                  2                                                                                    ⋮                                                                                      G                  M                                                              ]                ⁢                  xe2x80x83                ⁢        I            =              [                                                            I                1                                                                                        I                2                                                                        ⋮                                                                          I                N                                                    ]            
With these definitions the linear relationship between the frequencies of the cells, F, and the shim currents, I, is expressed in matrix form by the following:
F=G+AI 
One object of the invention is to find the shim current values, which produce the same frequency, or the best approximation to the same frequency, in each cell.
A feature is the method of optimization applied when the number of independent shim coils N is equal to the number of probe cells M, wherein the matrix is square and has a unique inverse Axe2x88x921. To find the shim current values Ik, which produce the same frequency in each cell is the following matrix equation is solved by setting all values of Fj equal, i.e. set F1=F2=. . . =FM:
I=Axe2x88x921 (Fxe2x88x92G),
Wherein Axe2x88x921 is the inverse matrix of A, i.e. Axe2x88x921 A=1.
Another feature is the foregoing method being utilized when the number of shim coils N is equal to or greater than the number of probe cells M.
A further feature is the optimization method when the number of shim coils N is less than the number of probe cells M, and wherein the currents in each shim are calculated according to a least square mathematical operation, and the least error in the magnetic field values are obtained for each cell.
Another feature is wherein the method is used to optimize shims used in adjustment of magnetic fields in an imaging system wherein the magnetic field is supplied by a magnet, and the plurality of probe cells are disposed in the magnetic field and the shims are disposed close to the cells and within the magnetic field.
Another feature is use of the method in a liquid spectroscopy apparatus wherein the probe cells and the shim coils are utilized for a plurality of samples.